Question
Solve for theta in the equation cos(2theta-30degrees)=-0.7660 for -180<theta>180
Answers
GPT 3.5
To solve for theta, we can manipulate the equation and use the inverse cosine function, also known as arccosine.
Given: cos(2θ - 30°) = -0.7660
Rearranging the equation:
2θ - 30° = arccos(-0.7660)
Now, use the inverse cosine function on both sides of the equation:
θ = (arccos(-0.7660) + 30°) / 2
Using a calculator to approximate arccos(-0.7660):
θ ≈ (40.607° + 30°) / 2
θ ≈ 70.607° / 2
θ ≈ 35.3035°
Therefore, the solution for theta is approximately 35.3035°.
Given: cos(2θ - 30°) = -0.7660
Rearranging the equation:
2θ - 30° = arccos(-0.7660)
Now, use the inverse cosine function on both sides of the equation:
θ = (arccos(-0.7660) + 30°) / 2
Using a calculator to approximate arccos(-0.7660):
θ ≈ (40.607° + 30°) / 2
θ ≈ 70.607° / 2
θ ≈ 35.3035°
Therefore, the solution for theta is approximately 35.3035°.